Beginning in the 1970's, there began a serious interest in generalizations of quantum theory. The motivation was the following. Quantum theory was a linear theory; consisting of Hilbert spaces, linear Schrödinger evolution, and so on. In physics, however, we tend to view such linear theories as approximations to some complicated `non-linear' theory, rather than as fundamental theories in their own right. This begets the question of whether such a generalization might be appropriate for quantum theory as well. Thus the program of generalized quantum theory (GQT) was conceived.The origins of this program might be traced to the work of B. Mielnik [1]} aptly titled “Generalized Quantum Mechanics". See references therein for additional background. The chief aim was of finding some suitable non-linear `quantum theory' that might supersede the standard formulation, in a spirit similar to how general Riemannian space-times had come to supersede that of Minkowski in the treatment of gravity.
